Characterizations of lattice surfaces

• 成果类型: Article
• 署名作者: Smillie, John; Weiss, Barak
• 署名单位: Ben-Gurion University of the Negev; Cornell University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0236-0
• 发表日期: 2010
• 页码: 535-557
• 关键词: quadratic-differentials; teichmuller curves; billiards; geometry

摘要

We answer a question of Vorobets by showing that the lattice property for flat surfaces is equivalent to the existence of a positive lower bound for the areas of affine triangles. We show that the set of affine equivalence classes of lattice surfaces with a fixed positive lower bound for the areas of triangles is finite and we obtain explicit bounds on its cardinality. We deduce several other characterizations of the lattice property.